For some info, each airline has different standards, but in general it is the immigration of the country that is the problem, for the airlines contact them in advance but 100% defo is discharge your bottle and remove the regulator, this prevents any pressure build up and explosion, bottles with air in that are carried on aircraft have to be classed as dangerous goods, such as dive tanks, O2 bottles gas bottles blah blah.
But be warned from my most recent jaunt to canada, i had no problems until arriving in montreal where i was stopped and quized, i told the truth about my equipment, he changed my immigration card to firearm and left me there for a bit came back and asked if it was a suped up modified paintball gun, i said no he crossed out firearm and let me go with no problems, but at the tourny because my bottle was not canadian registered they would not fill it.
with euro tourneys there isnt usually a problem except GERMANY, all paintball markers have to be registered with the police, how you do this i dont know, but if you are stopped at customs and they find it unregistered they will take it and not return it, so you loose it forever, also on the road the police are the same.
The best you can do for germany and hope you get away with it is that the marker has to be in a locked case, or padlocked bag, and has to be carried completely seperate from the bottle, so seperate bag, not in same bag but detached.
And it always pays to have a pgi in your bag to show pictures if the words are to complicated for people to understand.
So ask in advance if your equipment is acceptable,
discharge bottle,
if asked directly tell them(unlikely as they dont seem to have a clue about the sport), otherwise you could loose the lot.and maybe face a charge.
But i normally just say im off to a sporting event,as the bag is normally a give away to something more than a beach holiday in stokholm.
Hope that helps